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Ludwig Eduard Boltzmann is responsible for a lot of equations
and in various fields, different equations are termed the
**Boltzmann equation**.

In the field of stellar structure, an equation giving
the count of atoms at different possible atomic excitation
levels is given the name, or sometimes
**Boltzmann relation** (which is also ambiguous). One form:

N^{i+1}g^{i+1}———— = ———— e^{-(Ei+1-Ei)/kT}N^{i}g^{i}

- N
^{i+1}, N^{i}- number density of two states of excitation i and i+1. - g
^{i+1}, g^{i}- quantum-mechanical degeneracy weights. - k - Boltzmann constant.
- T - temperature.

This equation is related to the **Boltzmann distribution**
(frequency of particles at various states,
*not* the same as the Maxwell-Boltzmann distribution,
which is the distribution of (say) the kinetic energy
of particles in (say) a gas) incorporating
a **Boltzmann factor** (e^{-(E1-E2)/kT})
giving the relative probability of two energy levels,
and relating the ratio of the two
terms, N_{x}/g_{x}
(the number of atoms in specific quantum state)
to it.

degeneracy weight

state of excitation

Stefan-Boltzmann constant (σ)

temperature